Example 3. Assume 10,000 office buildings, each building having 100 female employees, and each female employee having a 1/100 chance of developing breast cancer in a given year. How many buildings will have no cases at all in a given year? And how many will have six cases? Click on 1 in the "m (expected occurrences per trial)" box and on 10,000 in the "Number of Trials" box. Then click the COMPUTE button. The answer is that 3,679 building will have no cases at all, and five buildings will have six cases. Human nature being what it is, people will conclude that there must be something wrong with these five buildings, and seize on some unusual characteristic -- proximity to a power line, presence of mold, or some other such nonsense -- as an explanation. Lawsuits will be filed, and our slightly demented judiciary will conclude that "there must be something going on" with these buildings. And they are right, there is something going on -- it is called "Chance".
Of course, age, ethnicity, diet, and many other things affect the likelihood of developing breast cancer. Doesn't matter. These variables increase the odds of breast cancer in any given individual relative to group averages, but they are not fully deterministic in any given time interval. A large element of chance remains. Thus, if we had 10,000 buildings with 100 women in each and all women had the BRCA1 gene, we would expect more cases of breast cancer overall, but with similar extremes in individual buildings. Likewise, in the Motel Caswell case, we might expect indexpensive motels in high-crime areas to have more crimes than expensive motels in low-crime areas, but ceteris paribus, we would expect similar extremes in individual motels. Chance predicts these "surprising" results, and human nature, along with the U.S. failure to teach probability and statistics in our schools, predicts that they will be confounded with causality.
Finally, please note that when a 1 or zero is shown in the cumulative probability or expected trials field, it does not mean exactly zero or 1, just that the number is closer to zero or 1 than any number that can be displayed in the space available without resorting to floating point notation.
©Copyright 1997, 2006, 2013 Chuck Anesi all rights reserved